Anil Kumar Soni¹, Swati  ², Vishnu Kumar Sahu^3*
1Department of Chemistry, Shia Post Graduate College, Lucknow, India.
²Academy of Scientific and Innovative Research NPL, Chemical and Food BND Division, CSIR-National Physical Laboratory, New Delhi, India.
³Department of Chemistry, Maharani Lal Kunwari, Post Graduate College, Balrmpur, India.
DOI: 10.4236/ojapps.2025.151020   PDF    HTML   XML   36 Downloads   158 Views   Citations

Abstract

In this research work, atomic and molecular orbitals based analysis has been made to see electronic structure of platinum halides (platinum dichloride, platinum dibromide, platinum diiodide and platinum difluride). The geometry optimization and three dimensional (3D) modeling of the above mentioned species have been made on CAChe pro software. The results show: (i) The involvement of three p atomic orbitals is negligible as their summation values are very low in comparison to d orbital and considerably low with respect to s orbital. (ii) The study well support the Landis concepts of sdⁿ-hybridation (here n = 1) as bond angle and contributions of s-orbital and d-orbital of Pt(II) are maximum with negligible contribution of p-orbitals. (iii) These halides also support the cloud-expanding effect with experimental data and also follow the nephelauxetic effect. The result is in good agreement with experiment results that covalent character increases in the order: PtI₂ > PtBr₂ > PtCl₂ > PtF₂. (iv) And thus the study will help to fine tune the existing complexes of these halides.

Keywords

Platinum Dhalides, Mulliken Population Analysis, sd-Hybridization, Molecular Orbital Diagram

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1. Introduction

Mathematical treatment of various laws of physics and chemistry were too complex to be solved [1]. However, it is only possible by Walter Kohn, who has developed the mathematics and John Pople, who has made its quantum mechanical forms. Both scientists were jointly awarded Noble Prize in chemistry in 1998: Kohn for simplifying the mathematics in descriptions of bonding of atoms, and Pople for development of the computational quantum chemistry [2]-[4]. Day-to-day developments in theoretical and computational works make it possible to have a deeper insight in the sub-atomic nature of atoms, ions and molecules [5]-[7]. In this research work, atomic and molecular orbitals based analysis will be made to see electronic structure of platinum halides. Platinum forms compounds in 0, +2, +3, +4, +5 and +6 oxidation states. Main oxidation states of platinum are 0, +2 and +4, while +5 and +6 are shown by fluorides or fluoro-complexes, and +3 is usually in binuclear compounds with M-M bonds [8] [9]. The ability of platinum to exist in many oxidation states is an important property of this element, which plays an important role in its applications. Platinum readily forms coordinate complexes and these complexes have their applications in diverse fields [10]-[18]. Day-to-day expansion in the chemistry of platinum and its complexes is due to their applications directly or indirectly pre-requisite for many of today’s problems related to anticancer drugs, photochemistry [19]-[22], biological system [23]-[25], materials science [26] [27] and nanoscience [28]. This is due to its versatile electron-transfer pathways. Survey of literature shows that platinum and its compounds are now used as sensors and switches [29], as catalyst [30]-[33], as antimicrobial agents [25], as biomarkers [24], as metallopharmaceuticals in treatment of cancer [18]. Platinum based complex compounds have also been used as drugs to activate or help to generate redox reactions [34]-[36]. A survey of literature shows that designing new ligands that can complexes with platinum in different oxidation states can lead to the development of new materials [36]. For new materials of diverse applications, there is and will be a continuous step-by-step study to discover new ligands and their new platinum complex. These complex compounds can formed either from their simple compounds or by substitution reactions from pre-synthesized complex compounds. The development of new platinum-based materials is and will be an ongoing need for various fields of science and technology, and thus for society. It is difficult to synthesize new molecule and test their various properties in laboratory, because it involves huge expenditure and consumes enormous time. Now, chemistry together with physics and computer science has shifted from, how to make a molecule to what molecule to make, in other words, molecule design. The emergence of computational chemistry and various software, have given a quantitative nature to the relationship between molecule, its property, its synthesis and thus its various applications [37].

2. Materials and Methods

The study material are platinum (II) halides. Three simple platinum dihalides exist. These are platinum (II) chloride, platinum (II) bromide and platinum (II) iodide, except platinum(II) fluoride which does not exist. The adopted methods for various calculations of platinum dihalides are based on Mulliken’s population analysis [38]-[41]. Mulliken defined ${\varphi }_i$ (molecular orbital), $n_{r,i}$ (the contributions of electrons in each occupied MO) and n_r-s,i (overlap population that explain bonding, antibonding and nonbonding nature of bond), as below:

${\varphi }_i={\displaystyle \sum _{rk}{c}_{irk}{\chi }_{rk}}$ (1)

$n_{r,i}=n_i{c}_{ri}^2$ (2)

$n_{r-s,i}=n_i\left(2c_{ri}{c}_{si}{S}_{rs}\right)$ (3)

here $n_i$ is the number of electron in f, i = 1 - 17, $c_{ri}$ is the coefficient of atomic orbitals for Pt-atom, $c_{si}$ is the coefficient of AOs for other atom (X − 2 or X − 3) and $S_{rs}$ is the overlap integral between the two AOs (one of an atom Pt − 1 or X − 2 and one of another atom X − 2 or X − 3). In order to obtain minimum energy structure we optimized the geometry of each halide by opting Extended Hückel Theory (EHT) [42]. All the calculations were performed on CAChe software. From minimum energy structure we have extracted values of eigenvectors, overlap matrix and eigenvalues. By submitting the values of eigenvector and overlap matrix in Equation (3), we have derived the values of overlap population. And the summation of values of overlap population was obtained to describe bonding, nonbonding and antibonding molecular orbitals. After that using all above along with eigenvalues molecular orbital diagram has been drawn. Before all these we have also examine the nature and contribution of atomic orbitals and then their mixing (valence bond theory) or overlapping (molecular orbital theory). V.B. Theory and M.O. theory on their refinements gave same wave function for the molecule but they differ in their approximations only. Mulliken (1955) also correlated the bonded interaction of V.B.T. with positive overlap population and non-bonded repulsion of V.B.T. with negative population analysis [38]-[41].

3. Results and Discussion

A systematic molecular mechanics based investigation of bonding nature in platinum dihalides has been studied. Platinum dihalides, which are under investigation, are dichloride, dibromide, diiodide and difluoride (which do not exist but also studied to explain its unstability). After gaining minimum energy structures a quantitative atomic orbital (AO) and molecular orbital (MO) treatment have also been made on platinum halides to study (i) involvement of metal (n − 1)d-, ns- and np-orbitals in hybridizations and its type that has been used to get information related to shape (bond angle) and size (bond length); (ii) contribution of various AOs in the construction of MOs through LCAO approximation using values of eigenvector and overlap matrix; (iii) nature of MOs by distinguishing them in to bonding, nonbonding and antibonding MO through population analysis and (iv) molecular orbital energy diagram and its construction using eigenvalues and overlap-population contribution.

3.1. Platinum Dichloride

The optimized geometry as obtained from molecular mechanics method of platinum(II) chloride is given below (Figure 1).

Figure 1. Structure of PtCl₂.

The MOs of this molecule are formed by linear combination of nineorbitals (five 4d-orbitals, one 5s orbital and three 5p orbitals) from platinum and four orbitals (three 3p orbitals and one 3s orbital) from each chlorine atom as shown below

Pt-1 = 5dx^2_y², 5dz², 5dxy, 5dxz, 5dyz, 6s, 6px, 6py, 6pz = 9AOs

Cl-2 = 3s, 3px, 3py, 3pz = 4AOs

Cl-3 = 3s, 3px, 3py, 3pz = 4AOs

Total = 17AOs

In order to examine the contribution of various AOs in the formation of MOs the LCAO has been made. The 17 AOs on LCAO approximations give 17 MOs. The various AOs are represented by ‘χ’ and MOs by ‘f’. Thus, χ₁ − χ₉ are AOs of platinum (χ₁ = 6s, χ₂ = 6px, χ₃ = 6py, χ₄ = 6pz, χ₅ = 5dx² − y², χ₆ = 5dz², χ₇ = 5dxy, χ₈ = 5dxz, χ₉ = 5dyz) and χ₁₀ − χ₁₇ are AOs of chlorine (χ₁₀ = 3s, χ₁₁ = 3px, χ₁₂ = 3py, χ₁₃ = 3pz for Cl-2 and χ₁₄ = 3s, χ₁₅ = 3px, χ₁₆ = 3py, χ₁₇ = 3pz for Cl-3). The magnitude of contribution of various AOs (χ) in the formation of 17 MOs (f₁ to f₁₇) is demonstrated in Table 1(a). A close look at this table reflected that seven AOs (χ₂, χ₃, χ₄, χ₈, χ₉, χ₁₃, χ₁₇) have no contribution in the formation of 1^st MO (f₁) as these have zero coefficient values. And the rest ten AOs (χ₁, χ₅, χ₆, χ₇, χ₁₀, χ₁₁, χ₁₂, χ₁₄, χ₁₅, χ χ₁₅) have their contribution in f₁. By adopting same view the contributions AOs in f₂ to f₁₇ MOs can be describe.

3.2. Platinum Dibromide

The optimized geometry (Figure 2) as obtained from molecular mechanics method of platinum (II) bromide is given below.

Figure 2. Structure of PtBr₂.

The MOs of this molecule as formed by linear combination of nine orbitals (five 4d-orbitals, one 5s orbital and three 5p orbitals) from platinum and four orbitals (three 3p orbitals and one 3s orbital) from each bromine are shown below:

Pt-1 = 5dx² − y², 5dz², 5dxy, 5dxz, 5dyz, 6s, 6px, 6py, 6pz, = 9

Br-2 = 4s, 4px, 4py, 4pz = 4

Br-3 = 4s, 4px, 4py, 4pz = 4

Total = 17

Table 1. (a) Eigenvector values of atomic orbitals (χ) in molecular orbitals (f_i) of PtCl₂; (b) Eigenvector values of atomic orbitals (χ) in molecular orbitals (f_i) of PtBr₂; (c) Eigenvector values of atomic orbitals (χ) in molecular orbitals (f_i) of PtI₂; (d) Eigenvector values of atomic orbitals (χ) in molecular orbitals (f_i) of PtF₂.

(a)
Atom					f1			f2			f3			f4			f5			f6			f7			f8			f9			f10			f11			f12			f13		f14		f15		f16		f17
Pt-1		χ1			−0.0704			−0.0000			0.1786			0.0000			0.0000			0.0000			−0.0000			−0.0000			0.0000			0.0000			0.0000			0.0000			0.3897		0.0000		0.0000		−1.0938		0.0008
		χ2			−0.0000			0.0312			−0.0000			0.0000			0.0000			−0.1299			0.0032			−0.0000			−0.0000			0.0000			0.0000			0.0000			0.0000		−0.0505		0.0000		0.0007		1.3371
		χ3			0.0000			0.0015			−0.0000			−0.0000			−0.0000			−0.0065			−0.0649			0.0000			0.0000			0.0000			−0.0000			−0.0000			−0.0000		1.0163		0.0000		−0.0000		0.0665
		χ4			−0.0000			−0.0000			−0.0000			0.0000			−0.0000			0.0000			−0.0000			0.0650			−0.0000			0.0000			−0.0000			−0.0000			0.0000		0.0000		1.0175		−0.0000		0.0000
		χ5			−0.0621			−0.0000			0.2745			0.0402			−0.0000			−0.0000			−0.0000			0.0000			−0.0000			−0.4975			0.0000			−0.0913			−0.7688		−0.0000		0.0000		−0.3649		0.0003
		χ6			0.0360			−0.0000			−0.1593			−0.0000			−0.0000			−0.0000			0.0000			−0.0000			0.0000			−0.8660			0.0000			0.0000			0.4461		0.0000		−0.0000		0.2117		−0.0002
		χ7			−0.0062			0.0000			0.0274			−0.4030			−0.0001			−0.0000			0.0000			0.0000			0.0000			−0.0496			0.0001			0.9161			−0.0766		−0.0000		0.0000		−0.0364		0.0000
		χ8			−0.0000			0.0000			−0.0000			0.0001			−0.4045			0.0000			0.0000			−0.0000			−0.0497			0.0000			0.9195			−0.0001			0.0000		−0.0000		−0.0000		0.0000		−0.0000
		χ9			0.0000			0.0000			−0.0000			0.0000			−0.0201			−0.0000			−0.0000			−0.0000			0.9988			−0.0000			0.0457			0.0000			0.0000		0.0000		0.0000		0.0000		0.0000
Cl-2		χ10			−0.6839			0.6981			−0.1032			0.0000			0.0000			0.0385			0.0000			0.0000			0.0000			0.0000			0.0000			0.0000			0.0315		0.0000		−0.0000		0.2963		−0.3916
		χ11			−0.0122			0.0100			−0.5661			0.0306			0.0000			0.6562			0.0346			0.0000			−0.0000			−0.0000			0.0000			0.0176			−0.1621		0.0092		0.0000		−0.5579		0.5819
		χ12			−0.0006			0.0005			−0.0281			−0.6161			−0.0001			0.0326			−0.6953			0.0000			0.0000			−0.0000			−0.0000			−0.3546			−0.0081		−0.1852		−0.0000		−0.0277		0.0289
		χ13			0.0000			0.0000			−0.0000			0.0001			−0.6169			0.0000			0.0000			0.6962			−0.0000			0.0000			−0.3551			0.0000			−0.0000		0.0000		−0.1854		0.0000		0.0000
Cl-3		χ14			−0.6836			−0.6984			−0.1032			0.0000			−0.0000			−0.0385			0.0000			0.0000			−0.0000			0.0000			0.0000			0.0000			0.0315		0.0000		0.0000		0.2966		0.3910
		χ15			0.0122			0.0100			0.5660			−0.0306			−0.0000			0.6563			0.0346			0.0000			0.0000			−0.0000			0.0000			−0.0176			0.1621		0.0092		0.0000		0.5585		0.5811
		χ16			0.0006			0.0005			0.0281			0.6157			0.0001			0.0326			−0.6957			0.0000			0.0000			−0.0000			0.0000			0.3545			0.0081		−0.1851		0.0000		0.0278		0.0289
		χ17			0.0000			0.0000			0.0000			−0.0001			0.6165			0.0000			0.0000			0.6966			0.0000			0.0000			0.3549			−0.0000			0.0000		0.0000		−0.1853		0.0000		−0.0000
(b)
Atom						f1			f2			f3			f4			f5			f6			f7			f8			f9			f10			f11			f12		f13		f14		f15		f16		f17
Pt-1			χ1			0.0841			0.0000			−0.1732			0.0000			0.0000			0.0000			−0.0000			−0.0000			0.0000			0.0000			0.0000			0.0000		0.4114		0.0000		0.0000		1.0271		0.0025
			χ2			−0.0001			−0.0425			−0.0000			0.0000			0.0000			−0.1455			−0.0008			0.0061			−0.0000			0.0000			0.0000			0.0000		−0.0001		−0.0127		−0.1011		0.0023		−1.2428
			χ3			0.0000			0.0004			−0.0000			−0.0001			0.0000			0.0012			−0.0608			−0.0026			0.0000			0.0000			0.0001			−0.0000		−0.0000		−1.0088		0.0433		−0.0000		0.0104
			χ4			0.0000			0.0043			−0.0000			0.0000			−0.0001			0.0147			−0.0026			0.0605			−0.0000			0.0000			−0.0000			0.0001		0.0000		−0.0423		−1.0037		−0.0002		0.1256
			χ5			0.0786			0.0000			−0.3736			0.0099			0.0559			−0.0001			−0.0000			0.0000			0.0017			−0.5050			0.0132			0.0834		−0.7260		−0.0000		0.0000		0.3274		0.0009
			χ6			−0.0445			0.0000			0.2113			−0.0010			−0.0970			0.0000			0.0000			−0.0000			0.0000			−0.8573			0.0011			−0.1443		0.4107		0.0000		−0.0000		−0.1852		−0.0005
			χ7			−0.0013			0.0000			0.0063			0.5567			−0.0069			0.0000			−0.0001			0.0000			0.1005			0.0085			0.8286			0.0051		0.0122		0.0001		0.0000		−0.0055		0.0000
			χ8			−0.0159			0.0000			0.0755			0.0054			0.5483			0.0000			0.0000			0.0001			0.0083			−0.1000			−0.0071			0.8161		0.1468		−0.0000		0.0001		−0.0662		−0.0002
			χ9			0.0001			0.0000			−0.0006			−0.0563			−0.0040			0.0000			−0.0000			−0.0000			0.9949			0.0008			−0.0837			−0.0075		−0.0012		0.0000		0.0000		0.0006		0.0000
Br-2			χ10			0.6804			−0.6973			0.1205			0.0000			0.0000			0.0423			0.0000			0.0000			0.0000			0.0000			0.0000			0.0000		0.0230		0.0000		−0.0000		−0.2529		0.3213
			χ11			0.0064			−0.0102			0.5266			0.0052			0.0556			0.6480			−0.0089			0.0701			−0.0000			−0.0000			−0.0034			−0.0446		−0.2344		0.0019		0.0150		0.5279		−0.5245
			χ12			−0.0001			0.0001			−0.0044			0.5531			−0.0063			−0.0054			−0.6994			−0.0304			0.0000			−0.0000			−0.4433			−0.0031		0.0020		0.1499		−0.0064		−0.0044		0.0044
			χ13			−0.0006			0.0010			−0.0532			0.0058			0.5503			−0.0655			−0.0297			0.6959			−0.0000			0.0000			0.0035			−0.4411		0.0237		0.0063		0.1492		−0.0533		0.0530
Br-3			χ14			0.6820			0.6956			0.1207			0.0000			0.0000			−0.0424			0.0000			0.0000			−0.0000			0.0000			0.0000			0.0000		0.0230		0.0000		0.0000		−0.2521		−0.3230
			χ15			−0.0064			−0.0102			−0.5271			−0.0052			−0.0557			0.6474			−0.0088			0.0699			0.0000			−0.0000			0.0034			0.0447		0.2345		0.0019		0.0151		−0.5263		−0.5272
			χ16			0.0001			0.0001			0.0044			−0.5544			0.0064			−0.0054			−0.6977			−0.0304			0.0000			−0.0000			0.4442			0.0031		−0.0020		0.1503		−0.0065		0.0044		0.0044
			χ17			0.0006			0.0010			0.0533			−0.0059			−0.5516			−0.0654			−0.0296			0.6943			0.0000			0.0000			−0.0035			0.4420		−0.0237		0.0063		0.1495		0.0532		0.0533
(c)
Atom				f1			f2			f3			f4			f5			f6			f7			f8			f9			f10			f11			f12			f13		f14		f15		f16		f17
Pt-1	χ1			−0.1194			0.0000			−0.1678			0.0000			0.0000			0.0000			0.0000			0.0000			0.0000			0.0000			0.0000			0.0000			0.4042		0.0000		0.0000		−1.0097		0.0002
	χ2			0.0000			−0.0612			0.0000			0.0000			0.0000			0.1535			0.0055			−0.0012			0.0000			0.0000			0.0000			0.0000			0.0000		−0.0990		0.0225		0.0002		1.2035
	χ3			0.0000			0.0005			0.0000			0.0000			0.0000			−0.0013			−0.0078			−0.0552			0.0000			0.0000			0.0000			0.0000			0.0000		0.1418		0.9967		0.0000		−0.0101
	χ4			0.0000			0.0062			0.0000			0.0000			0.0000			−0.0155			0.0549			−0.0078			0.0000			0.0000			0.0000			0.0000			0.0000		−0.9918		0.1402		0.0000		−0.1216
	χ5			−0.1235			0.0000			−0.4048			−0.0627			−0.0213			0.0000			0.0000			0.0000			−0.0017			−0.5050			0.0209			0.0742			−0.7114		0.0000		0.0000		−0.2913		0.0001
	χ6			0.0699			0.0000			0.2289			0.1116			0.0184			0.0000			0.0000			0.0000			0.0000			−0.8573			−0.0145			−0.1310			0.4024		0.0000		0.0000		0.1648		0.0000
	χ7			0.0021			0.0000			0.0068			0.1065			−0.6408			0.0000			0.0000			0.0000			−0.1005			0.0085			0.7518			−0.0843			0.0119		0.0000		0.0000		0.0049		0.0000
	χ8			0.0250			0.0000			0.0818			−0.6314			−0.1033			0.0000			0.0000			0.0000			−0.0083			−0.1000			0.0811			0.7407			0.1438		0.0000		0.0000		0.0589		0.0000
	χ9			−0.0002			0.0000			−0.0007			−0.0054			0.0657			0.0000			0.0000			0.0001			−0.9949			0.0008			−0.0767			0.0022			−0.0012		0.0000		0.0000		−0.0005		0.0000
I-2	χ10			−0.6655			−0.6925			0.1701			0.0000			−0.0000			−0.0501			0.0000			0.0000			0.0000			0.0000			0.0000			0.0000			0.0247		0.0000		0.0000		0.2514		−0.3004
	χ11			0.0164			−0.0089			0.5111			−0.0494			−0.0124			−0.6459			0.0690			−0.0157			0.0000			0.0000			−0.0096			−0.0493			−0.2631		0.0128		−0.0029		−0.5128		0.5004
	χ12			−0.0001			0.0001			−0.0043			0.0823			−0.4980			0.0054			−0.0987			−0.6939			0.0000			0.0000			−0.4946			0.0550			0.0022		−0.0184		−0.1290		0.0043		−0.0042
	χ13			−0.0017			0.0009			−0.0517			−0.4956			−0.0815			0.0653			0.6905			−0.0976			0.0000			0.0000			−0.0544			−0.4922			0.0266		0.1284		−0.0182		0.0518		−0.0506
I-3	χ14			−0.6654			0.6927			0.1701			0.0000			0.0000			0.0501			0.0000			0.0000			0.0000			0.0000			0.0000			0.0000			0.0247		0.0000		0.0000		0.2514		0.3002
	χ15			−0.0164			−0.0089			−0.5111			0.0493			0.0124			−0.6460			0.0689			−0.0157			0.0000			0.0000			0.0096			0.0493			0.2631		0.0128		−0.0029		0.5129		0.5002
	χ16			0.0001			0.0001			0.0043			−0.0823			0.4979			0.0054			−0.0987			−0.6940			0.0000			0.0000			0.4946			−0.0550			−0.0022		−0.0184		−0.1290		−0.0043		−0.0042
	χ17			0.0017			0.0009			0.0516			0.4955			0.0815			0.0652			0.6906			−0.0976			0.0000			0.0000			0.0543			0.4921			−0.0266		0.1284		−0.0182		−0.0518		−0.0505
(d)
Atom				f1			f2			f3			f4			f5			f6			f7			f8			f9			f10			f11			f12			f13		f14		f15			f16		f17
Pt-1	χ1			−0.0229			−0.0000			0.0751			0.0000			0.0000			0.0000			−0.0000			−0.0000			0.0000			0.0000			0.0000			0.0000			0.3609		−0.0005		0.0000			0.9884		0.0000
	χ2			0.0000			−0.0024			0.0000			0.0000			0.0000			0.0470			0.0032			−0.0000			−0.0000			0.0000			0.0000			0.0000			0.0000		0.1013		−0.0020			0.0000		1.1344
	χ3			0.0000			−0.0000			0.0000			−0.0000			−0.0000			−0.0004			−0.0012			0.0188			0.0000			0.0000			−0.0000			−0.0000			−0.0000		0.0631		−1.0023			−0.0000		−0.0095
	χ4			0.0000			0.0002			0.0000			0.0000			−0.0000			−0.0048			−0.0188			−0.0012			−0.0000			0.0000			−0.0000			−0.0000			0.0000		0.9972		0.0636			0.0005		−0.1146
	χ5			−0.0270			−0.0000			0.1456			−0.0098			−0.0010			−0.0000			−0.0000			0.0000			−0.0017			−0.5050			0.0103			−0.1006			−0.7948		−0.0002		0.0000			0.3438		0.0000
	χ6			0.0153			−0.0000			−0.0824			0.0168			−0.0011			−0.0000			0.0000			−0.0000			0.0000			−0.8573			0.0108			0.1724			0.4496		0.0001		−0.0000			−0.1945		−0.0000
	χ7			0.0005			0.0000			−0.0024			−0.0060			−0.0965			−0.0000			0.0000			0.0000			−0.1005			0.0085			0.9902			−0.0604			0.0133		−0.0000		0.0000			−0.0058		0.0000
	χ8			0.0055			0.0000			−0.0294			−0.0950			0.0061			0.0000			0.0000			−0.0000			−0.0083			−0.1000			−0.0620			−0.9751			0.1606		−0.0000		−0.0000			−0.0695		−0.0000
	χ9			0.0000			0.0000			0.0002			0.0014			0.0097			−0.0000			−0.0000			−0.0000			−0.9949			0.0008			−0.0996			0.0144			−0.0013		0.0000		0.0000			0.0006		0.0000
F-2	χ10			−0.6995			0.7077			−0.0367			0.0000			0.0000			−0.0124			0.0000			0.0000			0.0000			0.0000			0.0000			0.0000			0.0471		0.0001		−0.0000			−0.2300		−0.3013
	χ11			−0.0044			−0.0044			−0.6640			−0.0701			−0.0014			−0.6929			−0.0711			0.0014			−0.0000			−0.0000			−0.0002			0.0114			−0.1374		−0.0082		0.0002			0.2663		0.2713
	χ12			0.0000			−0.0004			0.0056			−0.0440			−0.6981			0.0058			−0.0443			0.7043			0.0000			−0.0000			−0.1126			0.0070			0.0011		−0.0051		0.0804			−0.0022		−0.0023
	χ13			0.0004			0.0000			0.0670			−0.6946			0.0443			0.0695			−0.7007			−0.0447			−0.0000			0.0000			0.0070			0.1121			0.0139		−0.0800		−0.0051			−0.0269		−0.0274
F-3	χ14			−0.6995			0.0000			−0.0367			−0.0000			−0.0000			0.0124			0.0000			0.0000			−0.0000			0.0000			0.0000			−0.0000			0.0471		0.0001		0.0000			−0.2300		0.3013
	χ15			0.0044			−0.7078			0.6640			0.0711			0.0014			−0.6928			−0.0713			0.0014			0.0000			−0.0000			0.0002			−0.0114			0.1374		−0.0080		0.0002			−0.2663		0.2713
	χ16			−0.0000			0.0000			−0.0056			0.0440			0.6980			0.0058			−0.0443			0.7043			0.0000			−0.0000			0.1126			−0.0070			−0.0012		−0.0051		0.0804			0.0022		−0.0023
	χ17			−0.0004			0.0000			−0.0672			0.6944			−0.0443			0.0705			−0.7007			−0.0447			0.0000			0.0000			−0.0070			−0.1121			−0.0139		−0.0800		−0.0051			0.0269		−0.0274

In order to examine the contribution of various atomic orbitals in the formation of molecular orbitals the LCAO has been studied. The 17 AOs on LCAO approximations give 17 MOs. Thus, χ₁–χ₉ are AOs of platinum (χ₁ = 6s, χ₂ = 6px, χ₃ = 6py, χ₄ = 6pz, χ₅ = 5dx² − y², χ₆ = 5dz², χ₇ = 5dxy, χ₈ = 5dxz, χ₉ = 5dyz) and χ₁₀ – χ₁₇ are AOs of chlorine (χ₁₀ = 3s, χ₁₁ = 3px, χ₁₂ = 3py, χ₁₃ = 3pz for Br-2 and χ₁₄ = 3s, χ₁₅ = 3px, χ₁₆ = 3py, χ₁₇ = 3pz for Br-3).The magnitude of contribution of various AOs (χ) in the formation of 17 MOs (f₁ to f₁₇) is demonstrated in Table 1(b). A close look at this table reflected that six AOs (χ₂, χ₃, χ₄, χ₉, χ₁₃, χ₁₆) have no contribution in the formation of 1^st MO (f₁) as these have zero or near zero coefficient values. And the rest eleven AOs (χ₁, χ₅, χ₆, χ₇, χ₈, χ₁₀, χ₁₁, χ₁₃, χ₁₄, χ₁₅, χ₁₇) have their contribution inf₁. By adopting same view the contributions AOs in f₂ to f₁₇ MOs can be describe.

3.3. Platinum Diiodide

The optimized geometry (Figure 3) as obtained from molecular mechanics method of platinum(II) bromide is given below.

Figure 3. Structure of PtI₂.

The MOs of this molecule as formed by linear combination of nine orbitals (five 4d-orbitals, one 5s orbital and three 5p orbitals) from platinum and four orbitals (three 3p orbitals and one 3s orbital) from each bromine are shown below

Pt-1 = 5dx^2_y², 5dz², 5dxy, 5dxz, 5dyz, 6s, 6px, 6py, 6pz, = 9

I-2 = 4s, 4px, 4py, 4pz = 4

I-3 = 4s, 4px, 4py, 4pz = 4

Total= 17

In order to examine the contribution of various atomic orbitals in the formation of molecular orbitals, the LCAO has been studied. The 17 AOs on LCAO approximations give 17 MOs. Thus, χ₁–χ₉ are AOs of platinum (χ₁ = 6s, χ₂ = 6px, χ₃ = 6py, χ₄ = 6pz, χ₅ =5dx² − y², χ₆ = 5dz², χ₇ = 5dxy, χ₈ = 5dxz, χ₉ = 5dyz) and χ₁₀ – χ₁₇ are AOs of chlorine (χ₁₀ = 3s, χ₁₁ = 3px, χ₁₂ = 3py, χ₁₃ = 3pz for I-2 and χ₁₄ = 3s, χ₁₅ = 3px, χ₁₆ = 3py, χ₁₇ = 3pz for I-3). The magnitude of contribution of various AOs (χ) in the formation of 17 MOs (f₁ to f₁₇) is demonstrated in Table 1(c). A close look at this table reflected that seven AOs (χ₂, χ₃, χ₄, χ₉, χ₁₂, χ₁₃, χ₁₆) have no contribution in the formation of 1^st MO (f₁) as these have zero or near zero coefficient values. And the rest ten AOs (χ₁, χ₅, χ₆, χ₇, χ₈, χ₁₀, χ₁₁, χ₁₄, χ₁₅, χ₁₇) have their contribution in f₁. By adopting same view the contributions AOs in f₂ to f₁₇ MOs can be describe.

3.4. Platinum Difluoride

The optimized geometry (Figure 4) as obtained from molecular mechanics method of platinum(II) fluoride is given below.

Figure 4. Structure of PtF₂.

The MOs of this molecule as formed by linear combination of nine orbitals (five 4d-orbitals, one 5s orbital and three 5p orbitals) from platinum and four orbitals (three 2p orbitals and one 2s orbital) from each bromine are shown below

Pt-1 = 5dx² − y², 5dz², 5dxy, 5dxz, 5dyz, 6s, 6px, 6py, 6pz, = 9

F-2 = 2s, 2px, 2py, 2pz = 4

F-3 = 2s, 2px, 2py, 2pz = 4

Total = 17

In order to examine the contribution of various atomic orbitals in the formation of molecular orbitals the LCAO has been studied. The 17 AOs on LCAO approximations give 17 MOs. Thus, χ₁–χ₉ are AOs of platinum (χ₁ = 6s, χ₂ = 6px, χ₃ = 6py, χ₄ = 6pz, χ₅ = 5dx² − y², χ₆ = 5dz², χ₇ = 5dxy, χ₈ = 5dxz, χ₉ = 5dyz) and χ₁₀ − χ₁₇ are AOs of chlorine (χ₁₀ = 3s, χ₁₁ = 3px, χ₁₂ = 3py, χ₁₃ = 3pz for F-2 and χ₁₄ = 3s, χ₁₅ = 3px, χ₁₆ = 3py, χ₁₇ = 3pz for F-3). The magnitude of contribution of various AOs (χ) in the formation of 17 MOs (f₁ to f₁₇) is demonstrated in Table 1(d). A close look at this Table 1(d) reflected that nine AOs (χ₂, χ₃, χ₄, χ₇, χ₉, χ₁₂, χ₁₃, χ₁₆, χ₁₇) have no contribution in the formation of 1^st MO (f₁) as these have zero or near zero coefficient values. And the rest eight AOs (χ₁, χ₅, χ₆, χ₈, χ₁₀, χ₁₁, χ₁₄, χ₁₅) have their contribution in f₁. By adopting same view the contributions AOs in f₂ to f₁₇ MOs can be describe.

3.5. Role of Metal Orbital

The characteristics of transition metal (TM) elements are due to their d orbitals of (n − 1) shell and s and p orbitals of n shell. When atom of TM elements form compound they adopted either concept of bonded attraction and non-bonded repulsion of VB (Valence Bond) theory, and or positive and negative overlap populations of MO (Molecular Orbital) theory. In the first case they may undergo various type of hybridization that depends upon the oxidation state of TM and number and nature of combing atoms or ions, and in the second case formation of molecular orbital by LCAO approximation. At first we have to examine the extent of involvement of 4d, 5s and 5p AOs of Pt-1 in the formation of MOs in platinum dihalides. For this, values of coefficient ‘χ’ of 5d_z², 5d_xy, 5d_xz, 6s, 6p_x, 6p_y and 6p_z have been separately tabulated for each MO for each platinum halides and are given in Table 2(a)-(d), respectively. The ‘χ’ of non-bonding orbitals 5d_x2−y2(χ₅) and 5d_yz(χ₉) are excluded. To see the total involvement of seven AOs of Pt-1 in twelve MOs (f₁ − f₁₂), the coefficient value of each orbital has been added. The five vacant MOs (f₁₃ − f₁₇) are exempted here, as there is only 24e⁻ to be filled by Aufbau principle, Hund’s rule and Pauli’s exclusion principle and thus we

Table 2. (a) Coefficient values of 4dxy, 4dxz, 4dx² − y², 5s, 5px, 5py, 5pz AOs of PtCl₂; (b) Coefficient values of 4dxy, 4dxz, 4dx² − y², 5s, 5px, 5py, 5pz AOs of PtBr₂; (c) Coefficient values of 4dxy, 4dxz, 4dx² − y², 5s, 5px, 5py, 5pz AOs of PtI₂; (d) Coefficient values of 4dxy, 4dxz, 4dx² − y², 5s, 5px, 5py, 5pz AOs of PtF₂; (e) Summation values of various AOs of halides of Pt(II).

(a)
MOs	5dz2 (Pt-1)		5dxy (Pt-1)		5dxz (Pt-1)			6s (Pt-1)			6px (Pt-1)		6py (Pt-1)			6pz (Pt-1)
f1	0.0360		0.0062		0.0000			0.0704			0.0000		0.0000			0.0000
f2	0.0000		0.0000		0.0000			0.0000			0.0312		0.0015			0.0000
f3	0.1593		0.0274		0.0000			0.1786			0.0000		0.0000			0.0000
f4	0.0000		0.4030		0.0001			0.0000			0.0000		0.0000			0.0000
f5	0.0000		0.0001		0.4045			0.0000			0.0000		0.0000			0.0000
f6	0.0000		0.0000		0.0000			0.0000			0.1299		0.0065			0.0000
f7	0.0000		0.0000		0.0000			0.0000			0.0032		0.0649			0.0000
f8	0.0000		0.0000		0.0000			0.0000			0.0000		0.0000			0.0650
f9	0.0000		0.0000		0.0497			0.0000			0.0000		0.0000			0.0000
f10	0.8660		0.0496		0.0000			0.0000			0.0000		0.0000			0.0000
f11	0.0000		0.0001		0.9195			0.0000			0.0000		0.0000			0.0000
f12	0.0000		0.9161		0.0001			0.0000			0.0000		0.0000			0.0000
Σ=	1.0613		1.4025		1.3739			0.2490			0.1643		0.0729			0.0650
(b)
MOs	5dz2 (Pt-1)		5dxy (Pt-1)		5dxz (Pt-1)			6s (Pt-1)			6px (Pt-1)		6py (Pt-1)			6pz (Pt-1)
f1	0.0445		0.0013		0.0159			0.0841			0.0001		0.0000			0.0000
f2	0.0000		0.0000		0.0000			0.0000			0.0425		0.0004			0.0043
f3	0.2113		0.0063		0.0755			0.1732			0.0000		0.0000			0.0000
f4	0.0010		0.5567		0.0054			0.0000			0.0000		0.0001			0.0000
f5	0.0970		0.0069		0.5483			0.0000			0.0000		0.0000			0.0001
f6	0.0000		0.0000		0.0000			0.0000			0.1455		0.0012			0.0147
f7	0.0000		0.0001		0.0000			0.0000			0.0008		0.0608			0.0026
f8	0.0000		0.0000		0.0001			0.0000			0.0061		0.0026			0.0605
f9	0.0000		0.1005		0.0083			0.0000			0.0000		0.0000			0.0000
f10	0.8573		0.0085		0.1000			0.0000			0.0000		0.0000			0.0000
f11	0.0011		0.8286		0.0071			0.0000			0.0000		0.0001			0.0000
f12	0.1443		0.0051		0.8161			0.0000			0.0000		0.0000			0.0001
Σ =	1.3565		1.5140		1.5767			0.2573			0.1950		0.0652			0.0823
(c)
MOs	5dz2 (Pt-1)		5dxy (Pt-1)	5dxz (Pt-1)			6s (Pt-1)			6px (Pt-1)		6py (Pt-1)			6pz (Pt-1)
f1	0.0699		0.0021	0.0250			0.1194			0.0000		0.0000			0.0000
f2	0.0000		0.0000	0.0000			0.0000			0.0612		0.0005			0.0062
f3	0.2289		0.0068	0.0818			0.1678			0.0000		0.0000			0.0000
f4	0.1116		0.1065	0.6314			0.0000			0.0000		0.0000			0.0000
f5	0.0184		0.6408	0.1033			0.0000			0.0000		0.0000			0.0000
f6	0.0000		0.0000	0.0000			0.0000			0.1535		0.0013			0.0155
f7	0.0000		0.0000	0.0000			0.0000			0.0055		0.0078			0.0549
f8	0.0000		0.0000	0.0000			0.0000			0.0012		0.0552			0.0078
f9	0.0000		0.1005	0.0083			0.0000			0.0000		0.0000			0.0000
f10	0.8573		0.0085	0.1000			0.0000			0.0000		0.0000			0.0000
f11	0.0145		0.7518	0.0811			0.0000			0.0000		0.0000			0.0000
f12	0.1310		0.0843	0.7407			0.0000			0.0000		0.0000			0.0000
Σ=	1.4316		1.7013	1.7716			0.2872			0.2214		0.0648			0.0844
(d)
MOs	5dz2 (Pt-1)		5dxy (Pt-1)		5dxz (Pt-1)			6s (Pt-1)			6px (Pt-1)		6py (Pt-1)			6pz (Pt-1)
f1	0.0153		0.0005		0.0055			0.0229			0.0000		0.0000			0.0000
f2	0.0000		0.0000		0.0000			0.0000			0.0024		0.0000			0.0002
f3	0.0824		0.0024		0.0294			0.0751			0.0000		0.0000			0.0000
f4	0.0168		0.0060		0.0950			0.0000			0.0000		0.0000			0.0000
f5	0.0011		0.0965		0.0061			0.0000			0.0000		0.0000			0.0000
f6	0.0000		0.0000		0.0000			0.0000			0.0470		0.0004			0.0048
f7	0.0000		0.0000		0.0000			0.0000			0.0032		0.0012			0.0188
f8	0.0000		0.0000		0.0000			0.0000			0.0000		0.0188			0.0012
f9	0.0000		0.1005		0.0083			0.0000			0.0000		0.0000			0.0000
f10	0.8573		0.0085		0.1000			0.0000			0.0000		0.0000			0.0000
f11	0.0108		0.9902		0.0620			0.0000			0.0000		0.0000			0.0000
f12	0.1724		0.0604		0.9751			0.0000			0.0000		0.0000			0.0000
Σ =	1.1561		1.2650		1.2814			0.0980			0.0526		0.0204			0.0250
(e)
AO		Pt(II)Cl2				Pt(II)Br2			Pt(II)I2					Pt(II)F2
Σ5dz2		1.0613				1.3565			1.4316					1.1561
Σ5dxy		1.4025				1.5140			1.7013					1.2650
Σ5dxz		1.3739				1.5767			1.7716					1.2814
Σ6s		0.2490				0.2573			0.2872					0.0980
Σ6px		0.1643				0.1950			0.2214					0.0526
Σ6py		0.0729				0.0652			0.0648					0.0204
Σ6pz		0.0650				0.0823			0.0844					0.0250

considered only twelve MOs among seventeen MOs. The summation values of AOs in these twelve MOs have been placed at the bottom of each table (Table 2(a)-(d)), which clearly reflects maximum involvement is of 5d orbital. Next to this is 5s orbital. It is also predicted from the summation values of d orbital. The non-bonding orbitals must have lowest summation values (Σdx² – y² = 0.9656 and Σdyz = 1.0646 in PtCl₂, Σdx² – y² = 1.2117 and Σdyz = 1.1479in PtBr₂, Σdx² – y² = 1.2141 and Σdyz = 1.1467 in PtI₂ and Σdx² – y² = 0.8010 and Σdyz = 1.1210 in PtF₂). The involvement of three p orbitals are negligible as their summation values are very low in comparison to d orbital and considerably low with respect to s orbital.

From Table 2(e) and Figure 5, it is evident that the involvement of 5p orbital in Pt-X bond is insignificant and the main role is played by ‘ns’ and (n − 1)d orbital. It was Landis, who discovered sdⁿ-hybridization (n = 1 to 5) along with molecular shape and bond angles in his seminal publications. Further, he also explained co-relationship between sdⁿ-hybridization and its bond angle by plotting a graph between energy and bond angle as shown in Figure 6. This figure reflected that bond angle has two minima one below 90˚ and one above 90˚. This is because the energy curves are function of the bond angles. The bond angles as presented in Figure 1 that also hold up Landis concept sdⁿ hybridization when n = 1. Landis recommended that transition metals in their valency shell can accommodate only 12e⁻ (10e⁻ in five (n − 1)d orbitals and 2e⁻ in one ns-orbital). The 18e⁻ can be in their valency shell (10e⁻ in five (n − 1)d orbitals, 2e⁻ in one ns-orbital and 6e⁻ in three np orbitals). Further, a close look at the Table 2(e) and right side of the curves of Figure 1 clearly demonstrated that the summation values are highest in case of iodide and lowest in chloride. This is due to cloud expending of halides. For a given metal ion, the ability of ligands to induce this cloud expending increases according to nephelauxetic series: F⁻ < H₂O < NH₃ < en < ox < SCN < Cl⁻ < CN⁻ < Br⁻ < I⁻. Thus, iodide produces greater cloud expanding effect than bromide, which inturn produces higher than chloride in platinum diiodide, platinum dibromide and platinum dichloride, respectively. In other words the effective positive charge on Pt(II) is reduced greater by iodide and lesser by chloride. This result is in good agreement with nephelauxetic series of ligands [43]. This effect can further be related with difference in energy level of ns and np orbitals. These two orbitals differ in energy significantly. The energy difference ∆ε in s and p orbitals of chloride, bromide and iodide are not same. The s and p orbitals in iodide are close as compared to s and p orbitals of bromide and chloride, as shown below.

Energy (eV)	F	Cl	Br	I
εs	−1.4699	−0.9665	−0.8110	−0.6615
εp	−0.6651	−0.5218	−0.4814	−0.4867
∆εs-p	−0.8048	−0.4447	−0.3296	−0.1748

Figure 5. (a) Extent of involvement of metal orbitals in the formation of MOs of PtCl₂, (b) Extent of involvement of metal orbitals in the formation of MOs of PtCl₂, (c) Extent of involvement of metal orbitals in the formation of MOs of PtCl₂ and (d) Extent ofinvolvement of metal orbitals in the formation of MOs of PtCl₂.

Figure 6. Plot between energy and bond angle(Å) for sd-hybridization.

Iodide, in which s and p orbitals are much close causes greater nephelauxetic effect and thus increases the covalent bond character in the molecule. Percentage of ionic and covalent bond character of PtCl₂, PtBr₂ and PtI₂ has been calculated by solving equation “% ionic character = 16 × ∆χ + 3.5 × (∆χ)²”, and results are shown below:

Compound	PtF2	PtCl2	PtBr2	PtI2
% Ionic Character	37.32	16.79	12.50	6.59
% Covalent Character	62.69	83.21	87.50	93.41

The result is in good agreement with experiment results that covalent character increases in the order: PtI₂ > PtBr₂ > PtCl₂ > PtF₂.

3.6. Overlap Population Analysis

The shape of each MO (f₁ − f₁₇) has been determined by the relative magnitudes and signs of the different coefficients [38]. For this the Pt(II)X₂ has been decomposed into three parts: Pt-1, X − 1 and X − 2, and the MO of the complete system has been obtained by allowing the orbitals of Pt − 1 (5d, 6s, 6p), X − 1 (ns and np) and X − 2 (ns and np) to overlap. The possible overlaps between the various AOs of platinum (Pt − 1) and halogens (X − 2 and X − 2) in each MO will be 88, as describes. To solve Equation (3) for these 88 overlapsin MOs of platinum dihalides, we need eigenvector values ($c_{ri}$ and $c_{si}$ ), values of overlap matrix ($S_{rs}$ ) and number of electrons ($n_i$ ) in each MO. The eigenvector and overlap integral values for platinum dihalides have been taken from Table 1(a)-(d) and Table 3(a)-(d), respectively. The number of electrons is taken as two for f₁ to f₁₂ and zero for f₁₃

Table 3. (a) Overlap matrix or overlap integrals values (S_rs) of various overlaps of atomic orbitals of constituent atoms in PtCl₂; (b) Overlap matrix or overlap integrals values (S_rs) of various overlaps of atomic orbitals of constituent atoms in PtBr₂; (c) Overlap matrix or overlap integrals values (S_rs) of various overlaps of atomic orbitals of constituent atoms in PtI₂; (d) Overlap matrix or overlap integrals values (S_rs) of various overlaps of atomic orbitals of constituent atoms in PtF₂.

(a)
AOs	6s	6px	6py	6pz	5dx2 − y2	5dz2	5dxy	5dxz	5dyz	3s	3px	3py	3pz	3s	3px	3py	3pz
	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Cl-2)	(Cl-2)	(Cl-2)	(Cl-2)	(Cl-3)	(Cl-3)	(Cl-3)	(Cl-3)
6s (Pt-1)	1.0000
6px (Pt-1)	0.0000	1.0000
6py (Pt-1)	0.0000	0.0000	1.0000
6pz (Pt-1)	0.0000	0.0000	0.0000	1.0000
5dx2 − y2 (Pt-1)	0.0000	0.0000	0.0000	0.0000	1.0000
5dz2 (Pt-1)	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
5dxy (Pt-1)	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
5dxz (Pt-1)	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
5dyz (Pt-1)	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
3s (Cl-2)	0.1923	0.2789	0.0139	0.0000	0.0825	−0.0479	0.0082	0.0000	0.0000	1.0000
3px (Cl-2)	−0.3085	−0.3783	−0.0257	0.0000	−0.1183	0.0688	−0.0156	0.0000	0.0000	0.0000	1.0000
3py (Cl-2)	−0.0153	−0.0257	0.1367	0.0000	−0.0134	0.0034	0.0750	0.0000	0.0000	0.0000	0.0000	1.0000
3pz (Cl-2)	0.0000	0.0000	0.0000	0.1380	0.0000	0.0000	0.0000	0.0760	0.0038	0.0000	0.0000	0.0000	1.0000
3s (Cl-3)	0.1922	−0.2788	−0.0139	0.0000	0.0825	−0.0479	0.0082	0.0000	0.0000	0.0003	−0.0021	−0.0001	0.0000	1.0000
3px (Cl-3)	0.3085	−0.3783	−0.0257	0.0000	0.1182	−0.0688	0.0156	0.0000	0.0000	0.0021	−0.0088	−0.0005	0.0000	0.0000	1.0000
3py (Cl-3)	0.0153	−0.0257	0.1367	0.0000	0.0134	−0.0034	−0.0750	0.0000	0.0000	0.0001	−0.0005	0.0009	0.0000	0.0000	0.0000	1.0000
3pz (Cl-3)	0.0000	0.0000	0.0000	0.1380	0.0000	0.0000	0.0000	−0.0760	−0.0038	0.0000	0.0000	0.0000	0.0009	0.0000	0.0000	0.0000	1.0000
(b)
AOs	6s	6px	6py	6pz	5dx2 − y2	5dz2	5dxy	5dxz	5dyz	4s	4px	4py	4pz	4s	4px	4py	4pz
	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Br-2)	(Br-2)	(Br-2)	(Br-2)	(Br-3)	(Br-3)	(Br-3)	(Br-3)
6s (Pt-1)	1.0000
6px (Pt-1)	0.0000	1.0000
6py (Pt-1)	0.0000	0.0000	1.0000
6pz (Pt-1)	0.0000	0.0000	0.0000	1.0000
5dx2 − y2 (Pt-1)	0.0000	0.0000	0.0000	0.0000	1.0000
5dz2 (Pt-1)	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
5dxy (Pt-1)	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
5dxz (Pt-1)	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
5dyz (Pt-1)	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
4s (Br-2)	0.1612	0.2376	−0.0020	−0.0240	0.0691	−0.0391	−0.0012	−0.0140	0.0001	1.0000
4px (Br-2)	−0.2686	−0.3511	0.0038	0.0463	−0.1101	0.0616	0.0023	0.0282	−0.0003	0.0000	1.0000
4py (Br-2)	0.0022	0.0038	0.1066	−0.0004	0.0019	−0.0005	0.0589	−0.0003	−0.0059	0.0000	0.0000	1.0000
4pz (Br-2)	0.0271	0.0463	−0.0004	0.1019	0.0171	−0.0165	−0.0003	0.0554	−0.0005	0.0000	0.0000	0.0000	1.0000
4s (Br-3)	0.1615	−0.2380	0.0020	0.0241	0.0692	−0.0392	−0.0012	−0.0140	0.0001	0.0001	−0.0006	0.0000	0.0001	1.0000
4px (Br-3)	0.2689	−0.3514	0.0038	0.0463	0.1103	−0.0617	−0.0023	−0.0283	0.0003	0.0006	−0.0028	0.0000	0.0003	0.0000	1.0000
4py (Br-3)	−0.0023	0.0038	0.1068	−0.0004	−0.0019	0.0005	−0.0590	0.0003	0.0060	0.0000	0.0000	0.0002	0.0000	0.0000	0.0000	1.0000
4pz (Br-3)	−0.0272	0.0463	−0.0004	0.1021	−0.0171	0.0166	0.0003	−0.0556	0.0005	−0.0001	0.0003	0.0000	0.0002	0.0000	0.0000	0.0000	1.0000
(c)
AOs	6s	6px	6py	6pz	5dx2 − y2	5dz2	5dxy	5dxz	5dyz	5s	5px	5py	5pz	5s	5px	5py	5pz
	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(I-2)	(I-2)	(I-2)	(I-2)	(I-3)	(I-3)	(I-3)	(I-3)
6s (Pt-1)	1.0000
6px (Pt-1)	0.0000	1.0000
6py (Pt-1)	0.0000	0.0000	1.0000
6pz (Pt-1)	0.0000	0.0000	0.0000	1.0000
5dx2 − y2 (Pt-1)	0.0000	0.0000	0.0000	0.0000	1.0000
5dz2 (Pt-1)	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
5dxy (Pt-1)	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
5dxz (Pt-1)	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
5dyz (Pt-1)	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
5s (I-2)	0.1516	0.2190	−0.0018	−0.0221	0.0611	−0.0346	−0.0010	−0.0123	0.0001	1.0000
5px (I-2)	−0.2549	−0.3361	0.0036	0.0431	−0.0999	0.0559	0.0021	0.0251	−0.0003	0.0000	1.0000
5py (I-2)	0.0021	0.0036	0.0906	−0.0004	0.0016	−0.0005	0.0484	−0.0003	−0.0049	0.0000	0.0000	1.0000
5pz (I-2)	0.0258	0.0431	−0.0004	0.0863	0.0150	−0.0141	−0.0003	0.0454	−0.0004	0.0000	0.0000	0.0000	1.0000
5s (I-3)	0.1515	−0.2190	0.0018	0.0221	0.0611	−0.0345	−0.0010	−0.0123	0.0001	0.0001	−0.0005	0.0000	0.0000	1.0000
5px (I-3)	0.2549	−0.3360	0.0036	0.0431	0.0999	−0.0559	−0.0021	−0.0251	0.0003	0.0005	−0.0019	0.0000	0.0002	0.0000	1.0000
5py (I-3)	−0.0021	0.0036	0.0906	−0.0004	−0.0016	0.0005	−0.0484	0.0003	0.0049	0.0000	0.0000	0.0001	0.0000	0.0000	0.0000	1.0000
5pz (I-3)	−0.0258	0.0431	−0.0004	0.0863	−0.0150	0.0141	0.0003	−0.0454	0.0004	0.0000	0.0002	0.0000	0.0001	0.0000	0.0000	0.0000	1.0000
(d)
AOs	6s	6px	6py	6pz	5dx2 − y2	5dz2	5dxy	5dxz	5dyz	2s	2px	2py	2pz	3s	2px	2py	2pz
	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(Pt-1)	(F-2)	(F-2)	(F-2)	(F-2)	(F-3)	(F-3)	(F-3)	(F-3)
6s (Pt-1)	1.0000
6px (Pt-1)	0.0000	1.0000
6py (Pt-1)	0.0000	0.0000	1.0000
6pz (Pt-1)	0.0000	0.0000	0.0000	1.0000
5dx2 − y2 (Pt-1)	0.0000	0.0000	0.0000	0.0000	1.0000
5dz2 (Pt-1)	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
5dxy (Pt-1)	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
5dxz (Pt-1)	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
5dyz (Pt-1)	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
2s (F-2)	0.1701	0.2642	−0.0022	−0.0267	0.0876	−0.0495	−0.0015	−0.0177	0.0001	1.0000
2px (F-2)	−0.1400	−0.2106	0.0023	0.0280	−0.0901	0.0505	0.0019	0.0227	−0.0002	0.0000	1.0000
2py (F-2)	0.0012	0.0023	0.0669	−0.0002	0.0015	−0.0004	0.0442	−0.0002	−0.0045	0.0000	0.0000	1.0000
2pz (F-2)	0.0141	0.0280	−0.0002	0.0641	0.0136	−0.0128	−0.0002	0.0414	−0.0003	0.0000	0.0000	0.0000	1.0000
2s (F-3)	0.1701	−0.2641	0.0022	0.0267	0.0876	−0.0495	−0.0015	−0.0177	0.0001	0.0000	0.0000	0.0000	0.0000	1.0000
2px (F-3)	0.1400	−0.2106	0.0023	0.0281	0.0901	−0.0505	−0.0019	−0.0227	0.0002	0.0000	−0.0001	0.0000	0.0000	0.0000	1.0000
2py (F-3)	−0.0012	0.0023	0.0669	−0.0002	−0.0015	0.0004	−0.0442	0.0002	0.0045	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000
2pz (F-3)	−0.0142	0.0281	−0.0002	0.0641	−0.0136	0.0128	0.0002	−0.0414	0.0003	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	1.0000

to f₁₇. Finally, Equation (3) has been solved for twelve MOs with respect to each halide. In order to get a precise description, the sums of overlap population for the eleven MOs of platinum halides have also been worked out and results are presented in Table 4(a)-(d). As can be seen from the table that among the twelve molecular orbital, eight are bonding, two are nonbonding and two are antibonding. The bonding molecular orbitals are f₁ − f₈. The nonbonding molecular orbital are f₉ and f₁₀, which are purely two d atomic orbitals of platinum namely dx² − y² and dyz. The antibonding molecular orbital are f₁₁ − f₁₂. A comparative study of Table 4(a)-(d) reflected that in all cases the non-bonding electrons are present in 9^th and 10^th molecular orbitals. Further, similarity in positions of nonbonding molecular orbitals prompted us to examine the eigenvalues of Pt⁺² ion and to compare them with the eigenvalues of the halides. The eigenvalues of the molecular orbitals of all the halides are included in Table 5, which shows that nonbonding orbitals are degenerate in all the cases.

Table 4. (a) Quantitative and qualitative nature of occupied molecular orbitals of platinum dichloride; (b) Quantitative and qualitative nature of occupied molecular orbitals of platinum dibromide; (c) Quantitative and qualitative nature of occupied molecular orbitals of platinum diiodide; (d) Quantitative and qualitative nature of occupied molecular orbitals of platinum difluoride.

(a)
MO No.		Σnr-s,i	Sign	MOs
f1		0.0545	+	BMO
f2		0.0236	+	BMO
f3		0.0022	+	BMO
f4		0.0753	+	BMO
f5		0.0753	+	BMO
f6		0.1168	+	BMO
f7		0.0259	+	BMO
f8		0.0259	+	BMO
f9		0.0000	0	NBO
f10		0.0000	0	NBO
f11		−0.0997	-	ABMO
f12		−0.0992	-	ABMO
(b)
MO No.		Σnr−s,i	Sign	MOs
f1		0.0563	+	BMO
f2		0.0277	+	BMO
f3		0.1901	+	BMO
f4		0.0734	+	BMO
f5		0.0733	+	BMO
f6		0.1273	+	BMO
f7		0.0184	+	BMO
f8		0.0184	+	BMO
f9		0.0000	0	NBO
f10		0.0000	0	NBO
f11		−0.0877	-	ABMO
f12		−0.0877	-	ABMO
(c)
MO No.	Σnr−s,i		Sign	MOs
f1	0.0788		+	BMO
f2	0.0367		+	BMO
f3	0.1632		+	BMO
f4	0.0641		+	BMO
f5	0.0641		+	BMO
f6	0.1280		+	BMO
f7	0.0143		+	BMO
f8	0.0143		+	BMO
f9	0.0000		0	NBO
f10	0.0000		0	NBO
f11	−0.0737		-	ABMO
f12	−0.0738		-	ABMO
(d)
MO No.	Σnr−s,i		Sign	MOs
f1	0.0198		+	BMO
f2	−0.0016		+	ABMO
f3	0.0720		+	BMO
f4	0.0121		+	BMO
f5	0.0121		+	BMO
f6	0.0275		+	BMO
f7	0.0035		+	BMO
f8	0.0036		+	BMO
f9	0.0000		0	NBO
f10	0.0000		0	NBO
f11	−0.0200		˗	ABMO
f12	−0.0200		˗	ABMO

MOs is molecular orbitals, BMO is bonding molecular orbital, ABMO is antibonding molecular orbital and NBO is nonbonding molecular orbitals.

Table 5. Energy (eV) of all the seventeen molecular orbitals of PtX₂.

MO No.	PtCl2	PtBr2	PtI2	PtF2
1	−0.9727	−0.8180	−0.6717	−1.4716
2	−0.9670	−0.8121	−0.6632	−1.4699
3	−0.5654	−0.5300	−0.5150	−0.6767
4	−0.5377	−0.5008	−0.4872	−0.6671
5	−0.5377	−0.5008	−0.4872	−0.6671
6	−0.5265	−0.4891	−0.4749	−0.6664
7	−0.5236	−0.4825	−0.4676	−0.6653
8	−0.5236	−0.4825	−0.4676	−0.6653
9a	−0.4627	−0.4627	−0.4627	−0.4627
10a	−0.4627	−0.4627	−0.4627	−0.4627
11	−0.4378	−0.4382	−0.4388	−0.4573
12	−0.4378	−0.4382	−0.4388	−0.4573
13	−0.4358	−0.4311	−0.4317	−0.4320
14	−0.1784	−0.1882	−0.1920	−0.1952
15	−0.1784	−0.1882	−0.1920	−0.1952
16	0.0366	−0.0863	−0.1277	−0.1682
17	0.3443	0.1528	0.0768	0.1074

^aThe energy nonbonding molecular orbitals are −0.4627, which is equivalent to the energy of degenerate d atomic orbitals (−0.4627 eV).

3.7. Molecular Orbital Diagram of Pt(II) Halides

In order to demonstrate the energy levels of different molecular orbitals, the position of nonbonding molecular orbitals and the magnitude of splitting of d orbitals, more precisely the molecular orbital diagram has been drawn separately for the four halides as Figures 7-10, respectively. The molecular orbital diagram is important in the sense that energy of each molecular orbital is shown which at a glance provides information about the difference in energies of various molecular orbitals and explains various properties of the molecule.

4. Conclusions

(i) The involvement of three p atomic orbitals is negligible as their summation values are very low in comparison to d orbital and considerably low with respect to s orbital. From Table 2(e) and Figure 5, it is evident that the involvement of 5p orbital in Pt-X bond is insignificant and the main role is played by “ns” and (n − 1)d orbital. Figure 6 reflected that bond angle has two minima one below 90˚ and one above 90˚. The study well supported the Landis concepts of sdⁿ-hybridation (here n = 1) as bond angle and contributions of s-orbital and d-orbital of Pt(II) are maximum with negligible contribution of p-orbitals.

Figure 7. MO diagram of PtCl₂along with energy of AOs and MOs in eV as show in parenthesis.

Figure 8. MO diagram of PtBr₂along with energy of AOs and MOs in eV as show in parenthesis.

Figure 9. MO diagram of PtI₂along with energy of AOs and MOs in eV as show in parenthesis.

Figure 10. MO diagram of PtF₂along with energy of AOs and MOs in eV as show in parenthesis.

(ii) These halides also support the cloud-expanding effect with experimental data and also follow the nephelauxetic effect. Table 2(e) and right side of the curves of Figure 5 clearly demonstrate that the summation values are highest in case of iodide and lowest in chloride (fluoride). This is due to cloud expending of halides. Thus, iodide produces greater cloud expanding effect than bromide, which inturn produces higher than chloride in platinum diiodide, platinum dibromide and platinum dichloride (platinum difluoride), respectively. In other words, the effective positive charge on Pt(II) is reduced greater by iodide and lesser by chloride (fluoride). This result is in good agreement with nephelauxetic series of ligands. This effect can further be related with difference in energy level of ns and np orbitals. These two orbitals differ in energy significantly. Iodide, in which s and p orbitals are much closer, causes greater nephelauxetic effect and thus increases the covalent bond character in the molecule. The result is in good agreement with experiment results that covalent character increases in the order: PtI₂ > PtBr₂ > PtCl₂ > PtF₂.

(iii) This study of atomistic details of halides of Pt(II) compounds and construction of molecular orbital diagram (Figures 6-10) that at a glance provide an insight of electronic behavior.

(iv) The study will help to fine tune the existing complexes of these halides.

Acknowledgements

I am very thankful to Principal and Head of Department of Chemistry, Shia P. G. College, Sitapur Road, Lucknow-226020 (U.P.) for laboratory facilities and also to Department of Higher Education, Prayagraj, Uttar Pradesh for financial assistance (Letter No./Reginal Office Lucknow/5496-99/2021-22; Dated: 15-03-2022 and G.O. No.-107/2021/2584/70-4-2021-4(28)/2021; Dated: 28-12-2021).